UN Secretary-General Ban- Ki moon is to arrive in Israel on Tuesday, and US Secretary of State John Kerry arrived in Cairo on Monday night amid a sudden spurt of intensive efforts to broker a Gaza cease-fire.

US President Barack Obama gave a strong push to the efforts on Monday, saying that the focus of both the US and the international community must now be on “bringing about a cease-fire that ends the fighting based on the 2012 cease-fire agreement between Israel and Hamas in Gaza.”

Obama reiterated Israel’s right to defend itself against rocket and tunnel attacks from Hamas, and said that “as a result of its operations, Israel has already done significant damage to Hamas’s terrorist infrastructure in Gaza.”

He also repeated his “serious concerns about the rising number of Palestinian civilian deaths and the loss of Israeli lives.”

Ban, who was due to meet Egyptian Foreign Minister Sameh Shoukry and Arab League Secretary-General Nabil Elaraby Monday evening, met with Kerry in Cairo before his scheduled trip to Israel.

During talks with Ban, Kerry said the United States would provide $47 million in humanitarian aid for Gaza.

Washington is "deeply concerned about the consequences of Israel's appropriate and legitimate effort to defend itself," Kerry said. "No country can stand by when rockets are attacking it."

"But always, in any kind of conflict, there is a concern about civilians - about children, women, communities that are caught in it," Kerry said.

Ban was also scheduled to meet Egyptian President Abdel Fattah al-Sisi.

Prime Minister Binyamin Netanyahu, in an interview with Sky News Arabic, pointed out that Israel accepted an Egyptian proposal for a ceasefire last week. That proposal called for an immediate end to the violence, followed 48 hours later by negotiations regarding a more lasting agreement. Part of the proposal called for Palestinian Authority security officers, rather than Hamas men, to man the border crossing with Rafah.

In addition to that proposal, Israel – Netanyahu said – also accepted shorter “humanitarian” cease-fires brokered over the last few days first by the UN, and then by the Red Cross. In each case, he said, Hamas violated the cease-fire.

“If Hamas really wants a cease-fire, I am sure that we can get to that,” he said. “But they don’t want one.”

One government official said that while Israel was ready for a cease fire, “Hamas cannot come out of a ceasefire looking like a victor. Israel would be skeptical of any proposal that could be seen as a victory for Hamas.”

Asked if relieving the naval blockade or opening the crossings would be interpreted in Jerusalem as a victory for Hamas, the official said that all the sanctions that have been clamped on Gaza were done as a function of the violence emanating from there.

“If there is no longer violence from Gaza,” the official said, “then certain things can be done. But the first thing is to stop the violence.”

If Netanyahu would agree to a cease-fire anytime soon, he would likely come up against stiff opposition from Foreign Minister Avigdor Liberman, who has called to take control of Gaza, and from Economy Minister Naftali Bennett.

Bennett, in a Channel 2 interview, made clear that he was opposed to ending the campaign until it was possible to say “the territory is clean.”

“It is impossible to finish the campaign without dealing with the tunnels,” he said. “The government defined the goals, and I don’t believe we will leave there until we restore security and quiet.”

Bennett said that Israel did not launch the campaign and pay a high price “to do half a job.”

Communications Minister Gilad Erdan, who like Bennett and Liberman is a member of the eight-person security cabinet, also voiced opposition to a cease-fire now.

“This is not the time to talk of a cease-fire,’’ he said. “We must complete the mission, and the mission cannot end until the threat of the tunnels is removed.”

Meanwhile, in the first meeting of its kind since the beginning of the current round of fighting, Palestinian Authority President Mahmoud Abbas and Hamas leader Khaled Mashaal met Monday in Qatar to discuss a possible cease-fire.

During the meeting, Abbas emphasized the need for all parties to abide by the recent Egyptian cease-fire initiative, a Palestinian official accompanying the PA president said.

The official said that Abbas and Mashaal agreed to continue consultations in order to “stop the Israeli aggression” on the Gaza Strip.

Abbas spokesman Nabil Abu Rudaineh reiterated the PA leadership’s call for an immediate cease-fire, saying this would “achieve the national goals of the Palestinian people.”

In the Gaza Strip, Hamas political leader Ismail Haniyeh said in a televised speech that his movement has decided to “end the blockade with its blood and weapons and there would be no return back.”

Haniyeh said Hamas’s conditions for a ceasefire include ending the blockade and Israeli “aggression” on the Gaza Strip and the release of former Palestinian prisoners who were rearrested by Israel in the past few weeks.

Early on Tuesday morning there were unconfirmed reports in the Arab media about a humanitarian cease-fire that would go into effect on Tuesday at 10:00 a.m. for five hours.
Reuters contributed to this report.